The only teams I follow are the Buckeyes in all things college sports.
When it comes to professional sports, I like to see our alumni do well, regardless of the team (i.e. if the Rams staring LB corps remains all Ohio State, I will probably follow their season closely).
NFL: My team in the is the Dolphins, but I am not nearly as passionate about them as I am the Buckeyes. Do I like it when then do well? Yes. Does it pain me when they lose? Not so much.
I also follow the Browns somewhat because I grew up in Mansfield (which was a big Browns town at the time), was around when Model bitched-out and ran off in the night, and was at the Draft Party at the Rock and Roll HOF when they got that future HOF'er Couch (ex-in-laws live in Parma Heights and are big time Browns fans), but I have always liked the Dolphins more since I can remember.
MLB: (Indians) Lost me years ago when they last struck and I really could not care less about it anymore, but I will snag our company seats (2 rows behind the Marlins' owner) once in awhile to take my son to a game.
NBA: Never had a favorite team, and never really followed it until the playoffs. I was rooting for the Cavs way back when because I wanted to see MJ and the Bulls lose those couple of years in the playoffs, but I just never got into the NBA all that much. I know I will get blasted for this, but I am glad that LeBron is in Miami with Wade and Bosch, because I will get to take my son to see them with company tickets as well.
NHL: I never got into hockey enough to have a team (but it is fun as hell to watch live from right behind the glass!).